A Chess Playing Program for the
IBM 704
A. BERNSTEIN
M. DE V. ROBERTS
NONMEMBER AlEE
NONMEMER AlEE
T. ARBUCKLE
M. A. BELSKY
NONMEMBER AlEE
NONMEMBER AlEE
HIS paper describes the program
which enables a human being to playa
game of chess with the InternationalBusiness Machines Corporation (IBM) 704
computer. The machine may. play either
white or black, and is capable of playing
a complete game of chess, including such
moves as castling, promoting, and capturing en passant.
The program is divided into five parts:
(1). Input-output, (2). Table generation,
(3). Evaluation, (4). Decision, and (5).
Tree
T
Input-Output
The input-output section of the program allows the human player to state his
moves to the machine in the normal
English notation on punched cards, for
example: P-K4 or B(Q4) X P(N7). The
program then translates this statement
into the machine notation for moves,
which gives the "to" square and the "from"
square with a code. A move in the
machine notation may also be entered
from the keys on the console.
The squares of the board are numbered
octally from 00 in the upper right-hand
corner of the board to 77 in the lower left.
For a regular move, the tag field contains
a 1, the decrement contains the "from
square" co-ordinates, the address contains the "to square" co-ordinates, and
the prefix contains a minus sign if the
move is a capture. For a castling move,
the tag field contains a 2, the decrement
contains the "to square" of the king, the
address contains 77 if castling up, a if
castling down, and the prefix is O. (Castling upwards means that the final position square of the king has a higher number than its initial square.) For an en
passant capture, the tag field is 3, the
decrement contains the "from square" of
the capturing pawn, the address contains
the "to square" of the capturing pawn,
and the prefix contains a minus sign. For
a promotion, the tag field contains a 4,
the decrement contains the "from square" .
of the pawn that promotes, the address
contains the "to square" on which pro-
motion occurs, and the prefix contains a
minus sign if the move is a capture.
At the start of a game the machine's
pieces always reside on the squares 00
to 07, 10 to 17; the opponent's on the
squares 60 to 67, 70 to 77.
If the machine were to play white and
make P-K4 as its first move, in machine
notation this would be the octal word,
0000 14100034.
When the machine has made a move,
or accepted an opponent's move, it prints
that move in the English notation, together with a picture of the board position, and makes a record of the move on
tape. At the end of the game the full
score is printed.
Table Generation
The table generating section accepts as
its input a table of the board position
which will be referred to as TAl. TAl
at the beginning of the game is arr~nged
so that it represents the starting position; but any board position may be
assembled into T A 1 and entered as the
starting position for the program.
TAl is 64 words long, one word per
square. The first word of T A 1 refers to
square 77, the last word to square 00. If
the square is empty then the word is all
zero. The word is negative if the square
is occupied by a machine piece. The address contains a number indicating
whether the piece is a king (5), queen
(0), rook (1), knight (4), bishop (2), or
pawn (3), and the decrement contains an
indexing quantity to link T A 1 with
Table 2, which will be called T A2.
T A2 is now generated from TAl in the
following form. It is 32 words long, one
per piece. The order is shown in Table 1.
A word in T A2 is of the following kind:
It is zero if the piece has been captured.
Otherwise, the address contains the value
of the piece, and the decrement contains
the co-ordinate of the square where the
piece is located. It can be seen that the
decrement of TA2 is the indexing quantity
of TAL
Table 31 and Table 32, called T A31
and T A32 are also g~nerated from TAL
T A31 refers to the machine and T A32
to the opponent. TA31 and TA32 are
similar in nature and function. Thus it
is sufficient to describe TA31.
TA31 is 512-words long, eight words
per square. The first eight words refer
to square 77 and the last eight words refer
to square 00. Consider the eight words
referring to square (xy). If the square xy
is occupied, the eighth word is negative,
and contains a bit in the first position if it
is occupied by the machine but not if
occupied by the opponent. The address
of the eighth word contains:
1. The number of machine pieces which
may move into square xy if xy is empty.
The number of machine pieces which
may immediately capture an opponent's
piece situated on xy.
3. The number of machine pieces immediately defending a machine piece situated on xy.
2.
The location of the pieces described in the
address of the eighth word are in the
decrements of the words 8 through 1.
The address of the seventh word stands
for the number of doubled machine pieces
bearing on square xy, e.g. a rook behind a
rook bearing on xy, or a queen behind a
The location of these
bishop, etc.
doubled pieces are to be found in the
. addresses of the words 6 through 1.
It will be seen that the location of the
pieces bearing on xy is the indexing quantity needed to find that piece in T AI, while
each square xy in TA3 is eight times the
indexing quantity of TAL
All possible moves are now listed in
TA3, for each square has in it the
number and locations of all pieces which
may move into it.
The routine which generates T A3 also
examines the position for any possible
pieces pinned to the king, so that no
illegal moves are listed in TA3.
TA2 and TA3 are generated in an
average time of 89 milliseconds.
Evaluation
The evaluation routines calculate a
score for the machine and the opponent
based upon the following criteria:
1.
2.
3.
4.
Mobility
Area control
King defense
Material
A. BERNSTEIN and M. DEV. ROBERTS are with
International Business Machines Corporation,
New York, N. Y.
T. ARBUCKLE and M. A.
BELSKY are with The Service Bureau Corporation,
New York, N. Y.
Bernstein, Arbuckle, Roberts, Belsky-IBM 704
From the collection of the Computer History Museum (www.computerhistory.org)
157
The program counts the., humber of
'available moves for each side; the number of squares completely controlled by
each side; the number of controlled
sq uares around each king; and the
material count of each side.
These criteria are parametrized for
easy variation, so that different values
may be given to center squares, or to the
squares around the king. At present
criteria 1, 2, and 3 are added together
while 4 is multiplied by a large factor
before adding it to the total. This prevents the machine from sacrificing material, and encourages it to exchange when
it is ahead, as it considers the ratio of its
own and opponent's scores.
Decision Routines
The decision routines serve the function
of producing a set of moves to be considered for further analysis. The idea
behind these routines is to select a small
number of moves which are potentially
good (for strategic reasons) rather than to
eliminate from all possible moves the
much larger number which can be determined to be bad.
The decision routines examine the position and determine whether certain states
exist; if the answer is yes, certain moves
are generated. The questions af'ked
are:
Is the king in check?
(a). Can material be gained?
(b). Can material be lost?
(c). Can material be exchanged?
3. Is castling possible?
4. Can minor pieces be developed?
5. Can key squares be occupied? (Key
squares are those squares which are controlled by diagonally connected pawns.)
6. Can open files be occupied?
1.
2.
7.
8.
Can any pawns be moved?
Can any piece be moved?
If the answer to question 1 is yes, the
machine asks itself whether' it is chec~ed
by one or two pieces; this information is
obtained by observing the square xy on
which the king is located in T A32, the
address of word 8 will be 2, if a double
check exists and 1 if a single check. If it
is a double check the only possible answer
is a king move; the machine examines the
empty squares around the king for legality
of moves and if any of these moves are
possible, the move is constructed and
entered in the Plausible Move Table.
The routine then returns control of the
tree. If instead the king is in check by a
single piece, interpositions of pieces, and
the capture of the checking piece are
158
Table I
1 .......................... Machine King
2 .......................... Machine Queen
3. . . . . . . . . . . . . . . . . . . . . . . .. Machine Bishop
4 .......................... Machine Bishop
5 .......................... Machine Knight
6 .......................... Machine Knight
7 .......................... Machine Rook
8 .......................... Machine Rook
9 .......................... Machine Pawn
10 .......................... Machine Pawn
11,' ......................... Machine Pawn
12 .......................... Machine Pawn
13 .......................... Machine Pawn
14 .......................... Machine Pawn
15 .......................... Machine Pawn
16 ....... , .................. Machine Pawn
17 .......................... Opponent's King
18 .......................... Opponent's Queen
19 .......................... Opponent's Bishop
20 .......................... Opponent's Bishop
21 .......................... Opponent's Knight
22 .......................... Opponent's Knight
23 .......................... Opponent's Rook
24 ................. , ........ Opponent's Rook
25 •......................... Opponent's Pawn
26 .......................... Opponent's Pawn
27 .......................... Opponent's Pawn
28 .......................... Opponent's Pawn
29 .......................... Opponent's Pawn
30 .......................... Opponent's Pawn
31 .......................... Opponent's Pawn
32 .......................... Opponent's Pawn
considered, and if possible these moves
as well as the king moves are en tered in
the Plausible Move Table. Control
then returns to the tree.
If the answer to question 1 is no, the
program goes down to question 2 and if
the answer to 2 (a) is yes, lists those moves
which gain material in the Plausible
Move Table; if2(b) is yes, finds which
moves will take the attacked piece to
safety, enters them in the Plausible Move
Table, and if 2(c) is yes, will enter those
exchanges in the Plausible Move Table.
Whenever the Plausible Move Table is
filled, control goes back to the tree for
further examination. At the end of
question 2 if the Plausible Move Table is
not filled, question 3 is asked. If yes, the
castling move is constructed and entered
in the Plausible Move Table. If the
answer to question 3 was yes, then control
goes back to the tree. If no, control
goes to question 4, etc.
The reason for stopping the decision
routine, if castling is possible, is that the
castling move does very little to enhance
the score of a position, but is nevertheless
a very important element in bringing the
king to safety. Therefore, whenever
castling is possible no other alternatives
except for material exchanges are given,
and eventually, when there are no exchanges or pieces to be gotten out of
attack, the program is forced to castle.
The ordering of these routines is important. At the beginning of the game
questions 1, 2, and 3 are not applicable
and questions 4 and 7 are the only ones
that produce moves. In the middle
game, questions 2,5, and 6 bear the brunt
of the work. In the end game, questions
5, 6, 7, and 8 are most employed. This
ordering is arbitrary and will probably
require adjustment as experience and
more knowledge of the way the program
plays is gained.
The Plausible Move Table is iimited
by time and coding considerations to
seven.
The Tree
The tree is the master routine. It
operates in the following manner: Having
received a position, it asks for a score
of the position, and for the set of plausible
moves; executes the first move; gets a
score and asks the decision routine for a
set of plausible replies. I t performs the
first of these and repeats the procedure until it reaches the fourth level,
where it performs each of the opponent's moves, obtaining a score for
each. It now takes the maximum score
of this last set of plausible moves and
brings it down as the score of the move
made on the third level, undoes that
move on the third level, makes the second
move of that set and requests plausible
replies for the opponent. Xi performs
each of these, gets their score l and brings
back the maximum opponent score (its
own minimum score) for the second move.
In this fashion it examines· the full
tree, and determines which move will
maximize its score. -With a plausible
move set of seven, and depth,. of four
half-moves, this examination takes an
average of 8 minutes.
The tree has a selective mechanism
which can cut some branches to be
examined. This mechanism is based
upon the relative scores of each of the
plausible Jlloves, and will function efficiently only after the scoring parameters
are· well adjusted. When this selective
method is in operation only moves which
are greater or equal in score to the position ssore before the move was made
are allowed to be examined further (except
when no moves are better, in which case
it takes only the two highest scored
moves).
At present this makes the total time
for producing a move 2 minutes on the
average. The program plays more conservatively in this mode, but does not
allow certain moves which are definitely
good, and which are otherwise considered
and sometimes made.
Conclusions
The machine plays a passable amateur
game at present during the opening and
Bernstein, Arbuckle, Roberts, Belsky-IBM 704
From the collection of the Computer History Museum (www.computerhistory.org)
middle game. I t is weak toward the
end, but the authors believe that additions to the decision routine will remedy
the situation. There are several other
routines that cou1d be expanded, such as
defending pieces rather than moving them
away when attacked. All of these are,
however, demonstrable, and add little
to the entire scope of the program.
Self-adjustment routines are being considered, to change the vallie of parameters
after the loss of a game, and to change the
Applications of Digital Computers to
Problems in the Study of Vehicular Traffic
WALTER HOFFMAN
RICHARD PAVLEY
NONMEMBER AlEE
NONMEMBER AlEE
HE study of vehicular traffic on a
Tscientific basis is still in its infancy.
This is due to the enormity of the job.
Currently, research in this area is carried
on along two distinct lines. First, there
is the approach which attempts to study
traffic conditions in the small and gradually builds up to larger systems. This is
an approach which may accomplish the
desired goals, but from all current indications success in this area is distant.
The second approach is a study of
traffic problems in the large, meaning
a major metropolitan area. Clearly, the
methods which are being used today
are relatively crude; but constant research for new methods and improvement
of the old ones had led to results which
have been verified in actual traffic situations, and the predictions made have
agreed remarkably well with the observed data.
The research reported in this paper is
based on data obtained by the Detroit
Metropolitan Area Traffic Study in. 1953.
At that time a survey of existing traffic.
conditions was made under the direction
of Dr. ]. Douglas Carroll at a cost of one
million dollars. The survey consisted
of three parts: First, a suitably large
sample of the population of the metropolitan area was interviewed at home and
information was obtained as to the origins
and destinations, nature, and frequency
of· the trips which were made. Second,
the major truck and taxi companies were
consulted and the same kind of information was obtained from them. Third,
roadside interviewing stations were set
up and vehicles were stopped and drivers
were asked the origin and destination and
nature of their trips.
The metropolitan area which was
studied included the city of Detroit and
its suburbs, covering three counties, and
extended far enough beyond them to include those areas which could reasonably
be expected to play any part in the metropolitan Detroit area traffic picture at the
end of the forecast period, which was set
at 1980. The area was divided into 265
zones, and the survey data were expanded
to give the total number of trips between
any pair of zones for an average 24-hour
period. These results were then checked
by comparing actual traffic counts across
screen lines against computed traffic
volumes. It was found that the data
obtained from the traffic survey were uniformly about 10% low, and suitable adjustments were made. Thus, an accurate
picture of the existing traffic flow had
been obtained and the data were presented
in the form of a matrix of order 265.
The assumption was made that any trip
which originated in the metropolitan area
would retrace itself within a 24-hour
period so that the matrix mentioned
was symmetric with nonnegative integers
as entries. Thus, the element aij of the
matrix represents the number of vehicles
which make a trip between zones i andj.
The first problem which presented itself was the prediction. of this matrix for
some future date. It is well known that
the trip generating characteristics of the
given area depend on land use and on the
population of the area. Thus, it was a
relatively simple matter to predict the
growth of the number of trips for each of
the 265 zones. The difficult problem is
the distribution of the total number of
trips originating or terminating in a
given zone over the remaining zones.
There are a number of methods in use
which attempt to cope with this problem,
all of which are imperfect. The problem
can be stated mathematically as follows:
Given a real symmetric matrix with nonnegative integral entries, find a matrix
ordering in the decision routines, but
these are still in the talking stage. While
it is true that the machine makes the same
move given in the same position, there are
so many positions, that i~s play is not
predictable in a new situation.
of the same kind whose row sums are
prescribed. Unfortunately, this mathematical problem does not have a unique
solution. I ts formulation thus must be
revised to take into account the char acteristics of traffic flow. All of the methods
cutrently used operate in a similar fashion.
If the predicted trip volume betwee~
zones i andj is denoted by a'ij, then this
quantity must be influenced by the
growth factors g i and gj of both zones
which are involved. Thus aij must be
multiplied by some mean value of the appropriate growth factors. In practice, aij
is multiplied by both growth factors, after
which an adjustment is made by dividing
the product,which is thus formed by
some normalization factor, K. The various methods employed differ in the
choice of K. Regardless of how K is
chosen, the new matrix obtained by this
process w1l1 not have the correct row
sums. To obtain a matrix of the proper
kind the process is repeated, and after a
few iterations convergence is obtained.
The methods used vary in the number
of iterations required for convergence.
The method used at this laboratory was
developed by Dr. Carroll's staff and has
becom~ known as the Detroit Method.
The number K in this method is obtained
by dividing the sum of all matrix elements
at the end of any iteration into the
predetermined sum of the elements of the
final matrix. This method has beenimproved upon by choosing K as that factor
which w~ll give the total matrix sum
as prescribed at the end of any iteration.
It is clear that this will accelerate convergence.
Regardless of which method was used,
this explains how the traffic picture for
the entire metropolitan area is predicted.
A new problem is the pre?entation of
this large number of individual data
elements in an easily comprehensible form.
The accepted means of doing this is the
so-called trip-desire map. This is a map
of the area divided into areas of equal
traffic density by means of isolines.
Production of such a map involves a great
deal of labor. The usual procedure can
WALTER HOFFMAN and RICHARD PAVLEY are with
Wayne University, Detroit, Mich.
Hoffman, Pavley-Study of Vehicular Traffic
From the collection of the Computer History Museum (www.computerhistory.org)
159